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Hello and welcome back to the.

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Course on Machine Learning.

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This is Kirill Eremenko,
and in today's tutorial we're.

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Talking about the Naive Bayes classifier.

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This is a very interesting machine
learning algorithm.

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And today we're going to get to.

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Know it on a very intuitive level.

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And in line

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with the super data science mission,
which is making the complex simple.

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We're going to break down this complex
topic into simple steps and bite.

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Sized pieces of information.

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I've got some very exciting slides
prepared ahead, so.

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Let's dive straight into it.

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All right.

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So here we've got the Bayes theorem.

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And this is something we talked about
in the previous tutorials.

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So by now we should be quite. Comfortable
with the concept.

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How are we going to apply it to create a.

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Machine learning algorithm.

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Well let's have a look here.

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We've got a data set.

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So it has two features.

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It has X1 and x2.

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And there are two categories category.

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One which is red and category two
which is green.

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But instead of working with these abstract
terms, we're going to convert them into

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something that.

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We can understand a bit better,

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something that's a bit easier to operate
with or to talk about.

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So we're going to call the y.

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Variable x2 variable salary.

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And the x one variable is going to be h.

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So basically
we're representing observations or people.

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That are part of our data
set in terms of their age and salary.

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As you can see
we have 30 people here on this chart.

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And the categories we're going to replace
them with walks, meaning that person.

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Walks to work and green will be. Drive.

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That means that person drives to work.

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And so now we get to a problem
to the machine learning challenge that.

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We're going to be solving.

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What happens if we add a new observation,
a new data point into this set?

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How do we. Classify this new data point.

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So as you can tell, this is a supervised
machine learning algorithm

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because we're classifying something
based on previously known classes.

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And so the question is
is this person going to be.

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Classified as a person. Who walks to work?

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Or is this.

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Person going to be classified
as a person who drives to work?

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And the Naive Bayes.

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Algorithm is going.

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To help us solve this challenge.

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All right.
So how are we going to approach this?

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We need a plan of attack.

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It is going to be quite
a complex approach.

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But at the same time
we're going to break it down into.

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Steps and it'll all make sense.

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It'll be very easy to understand.

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So our plan of attack.

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We're going to take the Bayes
theorem and we're.

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Going to apply it twice.

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First time
we're going to apply it to find out

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what is the probability
that this person walks given his features.

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And x over here is the features
or represents the features.

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Of that data point.

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So let's go back to the visualization
here.

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So here.

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You can see that this is.

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Our new data point.
That person has a certain age.

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So let's say the age of that person
maybe is like 25 years old.

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And then they have a salary.

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So let's say this
salary is $30,000 per year.

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So those are features of this observation.

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Right now
we're only working with two variables

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just for simplicity's sake
so we. Can visualize.

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Things age and salary.

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But in reality there could be many many
many more features.

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There could be features on how many what
what industry they work in or how many

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years of education they have, or how long
they've had a driver's license for.

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And the things like kind of
how far away they live from work.

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So there could be lots of variables.

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But at the same time, right now

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we're only going to be dealing
with two age and salary.

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And regardless of how many variables you.

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Have, they will be called.

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And we're going to call them features.

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So given the features of X,
so given the age of.

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25 and the salary of $30,000,
and we'll talk in more detail

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about exactly what we mean by features
just in a moment.

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And so therefore this part represents
that person that we're trying to classify.

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What is the likelihood of a person
with those features x.

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So we know that we are taking somebody
for those features that we have

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in our new data point.

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What is the likelihood of them working.

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And then we've. Got the right side.

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So we're going to talk through
each one of these as we calculate them.

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But for now let's just give. Them
their names going from right to left.

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So this one on over here
is called the prior probability.

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And we're going to calculate that first
because it's the easiest to calculate.

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Next one is the marginal likelihood.

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And we're going to calculate that second.

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The third one is a livelihood.

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That's just the names that they have.

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And we're going to calculate that.

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Third and finally what we're looking for
is called the posterior probability.

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We're going to calculate that force.

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All right.

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So that's our plan of attack for step one.

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This is all still step one to calculate
the probability that somebody walks

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given those features x
that we see in our new data point.

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Next we're going to have step two where
we're going to calculate the probability

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that somebody drives given those features
x that we see in our new data point.

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And again here we'll have the probability
which will calculate first,

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then the marginal likelihood
then the likelihood.

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And then we'll get to posterior
probability.

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And finally we're going to compare
the probability that somebody walks

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given features x versus the probability
that somebody drives given features x.

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And then from there we'll decide
which class to put that new data point in.

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So as you can see the Naive Bayes
classifier is a probabilistic type

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of classifier

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because we first calculate

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the probabilities and then based on
probabilities, we're assigning a class.

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All right.

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So are you ready to perform these steps.

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It's going to be lots of fun.

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We're going to take it nice and easy
nice and slowly

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so that we understand everything.
And after

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this you're going to be very comfortable
with the Naive Bayes classifier.

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Step one. All right.
So here we have our visualization.

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Let's move it all to the left a little bit
so we.

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Can make some space.

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Now we're going to.

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Calculate the first probability
in our Bayes theorem.

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We're going to calculate the probability
that somebody walks right.

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Just the overall probability.
And what does that mean.

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That is the probability that somebody
walks without knowing anything about them.

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So we're just saying

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we're going to add a new observation
to our data set into here.

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But we don't know their age
and we don't know their salary.

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We're just going to put it somewhere.
Into our data set.

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What is the probability that this person.

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That we're adding to our database walks
to work?

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Well, it's very easy and straightforward.

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From here we don't have much choice.

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The only thing that we can do
is calculate the number of.

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Read observations,

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the number of people that actually walk
and divide by the overall number.

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So probability
that a person walks to work.

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Without any other knowledge.

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Is the number of workers,
number of people at work,

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which is these red dots divided
by the total number of observation.

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The green dots.

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So the gray dot is in participating
in these calculations.

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So here we have
probability of somebody walks is 1010

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red dots divided by 30 dots overall.

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All right.

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So that was easy.

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We've calculated the prior probability.

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Next we calculating
the marginal likelihood.

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And this is where things get interesting.

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So how do we calculate
the marginal likelihood.

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Let's have a look.

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Here's our dataset again.

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And the first thing we're you're going to
do is we're going to select a radius.

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And we're going to draw a circle
around our observation like that.

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Now this radius you need.

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To select on your own.

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You need to decide for your algorithm.

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This is going to be like
an input parameter or an algorithm.

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You can select less.
You can select it more.

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It's up to you.

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Now what does this radius do.

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Well what we're going to do is we're going
to first of all let's

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just to make things
easier, we're going to remove.

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Our dot for now
just so that it's not confusing us.

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And then we're.

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Going to look at all the.

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Points that are inside this radius.

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And what.

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We're saying here is.

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That all of the points inside the circle.

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Are we're going to deem them to be similar
in terms of features, to the.

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Point that we had the point that we had.

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Remember, it had an age of, for example,
25 and a salary of $30,000 per year.

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So now we're going to draw
a radius around it.

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And let's say anybody between the ages
of 20 and 30 and in the salaries

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of $25,000 to $35,000,

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anybody that falls in that circle,
again, it's not a square.

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It's not just a square, it's a circle.

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anybody who falls somewhere,
somewhere in that.

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Vicinity is going to be deemed similar to.

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The new data point
that we're adding to our data set.

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So, as you can imagine,
this radius is actually going

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to have a big say in the way
your algorithm works.

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Well, let's say we have this radius and.

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This is how it all played out.

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We have three red dots
one green dot in there.

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All right.

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So now what do we do.

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How do we calculate the probability of x.

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And what is the probability of x.

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Well the probability of x
is the probability of a new point.

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That we add to our data set.

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Being similar in features to the.

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Point that we actually are adding to. It.

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So basically is the probability of.

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That new point that we're adding.

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Or like any random point
that we add, is the probability

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of that
any random point to fall into this circle.

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And p of x is calculated
as the number of similar observations.

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So the number of observations
that already. We can see in the circle.

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So one, two three, four divided by the
total number of observations which is 30.

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So p of x is four divided by three.

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Once again just to reiterate, p of x tells
us what is the likelihood of any new.

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Random variable that we add to this data
set falling inside this circle.

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And it is four over 30 because we only
have four, based on prior knowledge,

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we can tell that this four here
and this student also is four with three.

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All right.

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So that wasn't hard at all as well.

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We calculate the marginal likelihood.

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So so far we got this one
and we got this one.

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Next we're moving on to the likelihood.

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And this is probably the most complex one.

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What is the likelihood that somebody

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who walks exhibits features X.

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Well actually after we've spoken
about the marginal likelihood calculating.

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The likelihood won't be as. Complex.

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So let's have a look.

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So there's our chart.

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And now what we're.

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Going to do is we're going to.

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Draw the same circle again.

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And once again we're going to remove the.

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Gray point for now.

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And we're going to color our circle.

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And so.

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Anything that falls inside
the circle is deemed to be similar to the.

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Point that we're adding.

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So the question is
what is the probability.

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That a randomly selected data
point from our data.

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Set will be similar to.

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The data point that we're adding.

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So basically, what is the likelihood that
a randomly selected data point will be.

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From this circle?

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Given this vertical pipe means given that

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that person walks, that we know that
that person walks to work.

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The other way to think about

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this is we're only working
with people who walk to work.

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So we're only working with the red dots
which represent people who walk to work.

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So let's forget about the green dots
there like that.

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Now they're faint and we're not even
talking about them at all.

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We're only talking about the red dots.

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So the question is, given that we're only.

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Working with the red dots,
what is the likelihood that a

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randomly selected data point from our data

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00:10:32,266 --> 00:10:35,433
set, from the red dots, is somebody.

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Who exhibits features similar to.

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00:10:38,766 --> 00:10:41,400
The point that we are adding
to our data set.

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So basically, what is the likelihood
that a randomly selected

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red dot falls into this gray area,
into this circle?

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That's what the question we're asking.

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And that is also very simple.

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Now that we know how
all of this works, it's basically

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the number of similar observations
among those who work.

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So the number of red dots
that actually fall inside this red circle.

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In this gray circle, that's three
divided by the total number of workers.

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So people and total
number of people who walk to work.

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And that is three over ten.

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There we go.

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So that's our P of the likelihood
of somebody exhibiting the feature similar

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to that data point that were about to add,
given that we're only selecting among

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the red dots.

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So that's three over ten.

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And that was our likelihood.

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So now if we plug all that in
so there we go.

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That likelihood is done.

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So if we plug all of that.

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In we'll get our posterior probability.

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So three over ten times
ten over 30 and divided by four over 30.

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So if we calculate that it'll give us 0.75

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00:11:39,533 --> 00:11:42,766
75% is the probability

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00:11:42,766 --> 00:11:46,633
that somebody that we put into the place
where we're putting. X.

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Is should be classified
as a person who walks to work.

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That was step
one was pretty intense, right.

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Pretty exciting
to calculate this value now.

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And the next step is step two.

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That's step one.
The next step is step two.

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To do the same thing for the likelihood
that somebody with.

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Features X.

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Will be classified or should be classified
as a person who drives to work.

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And here
I'm going to throw you a challenge.

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I'm going to challenge you
to pause this video.

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Or rewind back to find out,
to have the image in front of you

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and do these calculations yourself, to.

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Actually go through the.

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Same steps and perform
those. Calculations.

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If you'd like to see
and compare to my calculations.

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Then I'm going to put in another video
after this one.

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So another tutorial
after this one in the course.

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So you can just go to the next tutorial
and compare.

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Otherwise
I'm just going to show you the result now.

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So the result is one over 24 likelihood.

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Or let's start from the right.

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Prior probability is 20 over 30
and marginal likelihood remains

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unchanged for over 30.

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Likelihood changes to one over 20.

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So the probability of somebody
who exhibits features

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00:12:54,433 --> 00:12:58,200
X being a person who drives to work
is 25%.

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So that was step two.

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Now we're going to do step three.

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We're going to compare.

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00:13:02,766 --> 00:13:06,633
The probability
of somebody with features X

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00:13:06,933 --> 00:13:10,033
the probability of them being a person
who walks to work versus the probability

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00:13:10,033 --> 00:13:13,033
of somebody who features
X being a person who drives to work.

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00:13:13,100 --> 00:13:15,466
So it's 75% versus 25%.

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00:13:15,466 --> 00:13:18,100
And therefore
the first is greater in the second.

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00:13:18,100 --> 00:13:21,300
And therefore
it is more likely that that person.

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00:13:21,300 --> 00:13:23,233
With features X is.

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00:13:23,233 --> 00:13:27,133
Going to be a person who walks to work
than the person who drives to work.

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00:13:27,133 --> 00:13:30,766
So still a 25% chance
that that is a person who drives to work.

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00:13:31,033 --> 00:13:33,966
But percent chance
that it is a person who walks to.

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00:13:33,966 --> 00:13:37,400
Work is great, 75%
and therefore, we're going to classify

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00:13:37,600 --> 00:13:40,733
this point as a person who walks to work.

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00:13:41,366 --> 00:13:43,266
There we go. That is how the.

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00:13:43,266 --> 00:13:47,200
Naive Bayes algorithm in machine
learning works.

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00:13:47,600 --> 00:13:49,800
I hope you found this tutorial useful.

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00:13:49,800 --> 00:13:53,200
I was I'm pretty excited and pre
proud of these slides,

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00:13:53,200 --> 00:13:56,700
and hopefully this is a step
by step and simple.

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00:13:56,700 --> 00:13:59,100
Explanation of a complex concept.

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00:13:59,100 --> 00:14:00,766
And I look forward
to seeing you next time.

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00:14:00,766 --> 00:14:02,566
Until then, enjoy machine learning.